Understanding and intervention in the dynamic behavior of regulatory networks is at the heart of emerging efforts in the development of modern treatment of cancer. A serious limitation of much of the previous work in cancer network analysis and control is the assumption of an ergodic network topology;that is, the underlying assumption that the structure of gene regulatory networks is cycle-free and all states of the network communicate with each other. Although the ergodicity assumption pertains to a small class of gene regulatory networks, this assumption is incorrect for most regulatory networks. Indeed, if one adopts the widely-accepted hypothesis that cell types are characterized by attractors in gene regulatory networks, then the presence of multiple cell types implies that the networks must have multiple ergodic sets. The impact of dynamic analysis and control strategies that assume ergodicity when applied to nonergodic gene regulatory networks can be misleading. This project will develop minimal-perturbation intervention strategies to control gene regulatory networks, that are not necessarily ergodic, to desired cellular states corresponding to normal or benign attractors. The aim to introduce a minimal-perturbation control policy is designed to induce few changes in the network structure and thus minimize potential adverse effects as a consequence of the intervention strategy. In order to achieve this ambitious goal, the proposed project will develop a new mathematical framework for the solution of the inverse perturbation problem for ergodic and non-ergodic Markov chains;i.e. given a probability transition matrix and desired steady-state distribution, determine the minimal perturbation of the transition matrix that will converge to the desired distribution. The theoretical analysis will be complemented by a thorough experimental verification in the melanoma cell line: the investigators will design RNAi and plasmid molecules for regulation of the expression levels of specific genes of the melanoma network to test the results of the predicted model. PUBLIC HEALTH RELEVANCE: Bridging between mathematical analysis and biological experimentation as well as close cooperation among researchers from applied mathematics, engineering, and medicine is essential to establish an effective plan that will ultimately lead to the development of novel treatment and clinical decision-making in cancer research.